X3894

X549com[INVERSE(n(3rd EULER TRIANGLE))]

< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 21 }: Central Line L(1, 21) { 518, 599 }: Central Line L(518, 599) { 210, 942 }: Central Line L(210, 942) { 912, 1699 }: Central Line L(912, 1699) { 46, 3158 }: Central Line L(46, 3158) { 78, 3337 }: Central Line L(78, 3337) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_599 = ISOTOMIC CONJUGATE OF X(598) (0.4748, 0.1327) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_912 = -CEVA CONJUGATE OF X(3) (0.0031, -0.0428) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_3158 = -CEVA CONJUGATE OF X(9) (0.6726, 0.2916) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_3337 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(499) (0.6034, 0.2920) X_3894 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6830, 0.3799) A B C X1 X21 X518 X599 X210 X942 X912 X1699 X46 X3158 X78 X3337 X3894 (a, b, c) = (5, 6, 7) | AB = 1

X3894 (X549com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(2b^{3} + 2c^{3} - 2a^{2}b - 2a^{2}c - 3abc)\)
Search Value (6, 9, 13): \(-1.735254984542\)
▸ Incident Central Lines11 lines

{1, 21}, {46, 3158}, {65, 3632}, {72, 3624}, {78, 3337}, {210, 942}, {517, 3534}, {518, 599}, {912, 1699}, {2093, 3174}, {3555, 3633}